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A043547 Odd numbers interspersed with double the previous odd number. 10
1, 2, 3, 6, 5, 10, 7, 14, 9, 18, 11, 22, 13, 26, 15, 30, 17, 34, 19, 38, 21, 42, 23, 46, 25, 50, 27, 54, 29, 58, 31, 62, 33, 66, 35, 70, 37, 74, 39, 78, 41, 82, 43, 86, 45, 90, 47, 94, 49, 98, 51, 102, 53, 106, 55, 110, 57, 114, 59, 118, 61, 122, 63, 126, 65, 130, 67, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
As pointed out by E. Angelini on the SeqFan list (cf. link), this is the lexicographically earliest sequence of positive integers without repetitions such that the sum of four consecutive terms is always a multiple of 4. - M. F. Hasler, Mar 22 2013
LINKS
E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013
FORMULA
a(n) = (2 - n) * (n - floor(n/2) * 2) + 2 * (n - 1).
G.f.: x*(1+2*x)*(1+x^2)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003
a(2n-1) = 2n-1, a(2n) = 4n-2. - M. F. Hasler, Mar 22 2013
From Wesley Ivan Hurt, Nov 22 2015: (Start)
a(n) = 2*a(n-2) - a(n-4) for n>4.
a(n) = n*(-1)^n/2 - (-1)^n + 3*n/2 - 1. (End)
EXAMPLE
a(1)=1 because n is odd. a(2)=2 because a(1)*2=2.
MAPLE
A043547:=n->n*(-1)^n/2-(-1)^n+3*n/2-1: seq(A043547(n), n=1..100); # Wesley Ivan Hurt, Nov 22 2015
MATHEMATICA
Flatten[Table[Accumulate[{2 n - 1, 2 n - 1}], {n, 40}]] (* Wesley Ivan Hurt, Nov 22 2015 *)
With[{o=Range[1, 71, 2]}, Riffle[o, 2o]] (* Harvey P. Dale, Sep 17 2019 *)
PROG
(PARI) A043547(n)=n+!bittest(n, 0)*(n-2) \\ M. F. Hasler, Mar 22 2013
(Magma) [n*(-1)^n/2-(-1)^n+3*n/2-1 : n in [1..50]]; // Wesley Ivan Hurt, Nov 22 2015
(PARI) Vec(x*(1+2*x)*(1+x^2)/(1-x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 22 2015
CROSSREFS
For n>3, a(n) = A059029(n-3)+3. For n>1, a(n) = A022998(n-2)+2.
Sequence in context: A091239 A145110 A257405 * A338702 A064919 A064923
KEYWORD
easy,nonn
AUTHOR
Jim Cook (jcook(AT)halcyon.com), Mar 01 2000
EXTENSIONS
More terms from James A. Sellers, Mar 01 2000
STATUS
approved

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Last modified February 29 17:30 EST 2024. Contains 370428 sequences. (Running on oeis4.)